1. Find the distance from the point (1, 4, 1) to the plane 2x ...

The shortest distance from a point to a plane is along a line orthogonal to the plane. That is, it is in the direction of the normal vector. We can project the vector we found earlier onto the normal vector to nd the shortest vector from the point to the plane. If we let v = 2 4 1 4 0 3 5and n = 2 4 2 3 1 3 5, we can compute v n = (1)(2) + (4 ... ................
................